please answer this question​

Please Answer This Question

Answers

Answer 1

Answer:

[tex]a_n=3n-2[/tex]

Step-by-step explanation:

General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]

where:

[tex]a_n[/tex] is the nth term[tex]a[/tex] is the first term[tex]d[/tex] is the common difference between terms

Create expressions for the 4th and 6th terms:

[tex]\implies a_4=a+(4-1)d=a+3d[/tex]

[tex]\implies a_6=a+(6-1)d=a+5d[/tex]

The ratio of the 4th term to the 6th term is 5:8, therefore:

[tex]\implies \dfrac{a_4}{a_6}=\dfrac{5}{8}[/tex]

[tex]\implies \dfrac{a+3d}{a+5d}=\dfrac{5}{8}[/tex]

[tex]\implies 8(a+3d)=5(a+5d)[/tex]

[tex]\implies 8a+24d=5a+25d[/tex]

[tex]\implies 8a-5a=25d-24d[/tex]

[tex]\implies 3a=d \quad \leftarrow \textsf{Equation 1}[/tex]

Sum of the first n terms of an arithmetic series:

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

The sum of the first 7 terms of an arithmetic progression is 70:

[tex]\implies S_7=70[/tex]

[tex]\implies \dfrac{7}{2}[2a+(7-1)d]=70[/tex]

[tex]\implies 2a+6d=20[/tex]

[tex]\implies a+3d=10 \quad \leftarrow \textsf{Equation 2}[/tex]

Substitute Equation 1 into Equation 2 and solve for [tex]a[/tex]:

[tex]\implies a+3(3a)=10[/tex]

[tex]\implies a+9a=10[/tex]

[tex]\implies 10a=10[/tex]

[tex]\implies a=1[/tex]

Substitute found value of [tex]a[/tex] into Equation 1 and solve for [tex]d[/tex]:

[tex]\implies 3(1)=d[/tex]

[tex]\implies d=3[/tex]

Finally, substitute found values of [tex]a[/tex] and [tex]d[/tex] into the general form of the arithmetic sequence:

[tex]\implies a_n=1+(n-1)3[/tex]

[tex]\implies a_n=1+3n-3[/tex]

[tex]\implies a_n=3n-2[/tex]


Related Questions

Step 1: –10 + 8x < 6x – 4
Step 2: –10 < –2x – 4
Step 3: –6 < –2x
Step 4: ________

What is the final step in solving the inequality –2(5 – 4x) < 6x – 4?

x < –3
x > –3
x < 3
x > 3

Answers

x > 3

Step-by-step explanation:

The final step in solving the inequality –2(5 – 4x) < 6x – 4 is

-6/-2 < x = 3 < x

Which of the following are solutions to the inequality below? Select all that apply.

8 ≤ j j = 12 j = 5 j = 6 j =11

Answers

Answer:

    j = 11

    j = 12

Step-by-step explanation:

   The inequality:

8 ≤ j

   We will test all the options given.

-> In short, all options greater or equal to 8 will be solutions.

j = 12

8 ≤ j

8 ≤ 12 ✓

-

j = 5

8 ≤ j

8 ≤ 5 ✗

-

j = 6

8 ≤ j

8 ≤ 6 ✗

-

j =11

8 ≤ j

8 ≤ 11 ✓

Please help asap! Thanks

Answers

[tex]y=f(x)= \dfrac x 3 \\\\\text{Replace x with y and then solve for y,}\\\\~~~~x = \dfrac y 3\\\\\implies y = 3x \\\\\implies f^{-1}(x) =3x[/tex]

Points J, Q, K, and l are on the given circle. If Arc KL measures 120 degrees, and Angle KML measures 98 degrees, what is the measure of Arc JQ?

Answers

The value of the measure of Arc JQ from the given task content is; 142⁰.

What is the measure of Arc JQ?

The measure of Arc JQ can be evaluated by establishing a fact that; the total angle measure in a circle by convention is; 360⁰.

On this note, it follows that the measure of Arc JQ is; 360 - 120 - 98 is; 142.

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PLEASE HELP PLEASE PLEASE HELP

Answers

Answer:

2:3

Step-by-step explanation:

Simplica Los dos numeros

6 ÷ 3 = 2

9 ÷ 3 = 3

Suzy drove to a hair appointment at 50mph. Her average speed on the return home was 40mph. The return home took 1/4hr longer because of heavy traffic. How far did she travel to her hair appointment?

Answers

Since Suzy return took 1/4 hr longer, how far Suzy travelled to her appointment is 50 mi

To answer the question, we need to know what distance travelled by Suzy is

Distance between Suzy's home and hair appointment

The distance between Suzy and her appointment is d = vt where

v = Suzy's speed = 50 mph and t = time it takes to teach her appointment.

So, d = 50t   (1)

Now, since Suzy returns home at a speed of v' = 40 mph and takes her 1/4 hr longer to return home,her return time is , t' = (t + 1/4) h

Since the distance she ruturns home is the same, we also have that

d = v't'

= 40(t + 1/4)  (2)

Equating (1) and (2), we have

50t = 40(t + 1/4)

50t = 40t + 10

50t - 40t = 10

10t = 10

t = 10/10

t = 1 hr

How far Suzy travelled to her appointment

Substituting t = 1 into d = 50t, we have

d = 50(1)

d = 50 m

So, how far Suzy travelled to her appointment is 50 mi

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What is the equation of the circle with a radius of 7 and center at (6, -5)?
A (x + 6)2 + (y - 5)2 = 49
B (x - 6)2 + (y + 5)2 = 7
C (x + 6)2 + (y - 5)2 = 7
D (x - 6)2 + (y + 5)2 = 49

Answers

Answer:

D is the equation of the circle

Hey everyone
This' just a random math question
[tex]x + 5 - \cfrac{1}{3} = 12[/tex]

Answers

Answer:

The value of x = 22/3

Step-by-step explanation:

x + 5 - 1/3 = 12

=> x+5 = 12 + 1/3

=> x + 5 = (36 + 1) /3

=> x + 5 = 37 /3

=> (x+5) 3 = 37

=> 3x + 15 = 37

=> 3x = 37 -15

=> 3x = 22

=> x = 22/3

Answer to your question is given in the attachment

Hope this Helps :)

Find the volume of the rectangular prism.
8 cm
10 cm
2 cm
10 cm
OA. 160.5 cm³
B. 182.4 cm³
Oc. 181.4 cm³
D. 160 cm³
2 cm

Answers

Answer:

volume= lxbxh= 10*8*2= 160 cm3

Hello all, what is 8y = 89.

Answers

Answer:

y= 11. 125

Step-by-step explanation:

8 y = 89

because you do not have another y on the other side simple divide

8 y = 89

89 / 8 = y

y= 11. 125

(Not sure what decimal place to round to  so there are all 3 )

Hey there!


8y = 89

DIVIDE 8 to BOTH SIDES

8y/8 = 89/8

SIMPLIFY IT!
y = 89/8

y ≈ 11 1/8

y ≈ 11.125


Therefore, the answer is:

y = 89/8


Good luck on your assignment & enjoy your day!


~Amphitrite1040:)

I don’t understand and I need the answer

Answers

Answer:

y2 + 2y + 80

Step-by-step explanation:

Hope this helpd :) Mark brainliest?

Answer:-21

Step-by-step explanation:

-21 i think but im pretty sure

Show what you know: work out the problems below and submit a photo of your work to receive full credit.

The Florida A&M Rattlers are decorating campus for homecoming weekend. Students use 3 rolls of orange streamers for every 2 rolls of green streamers for every dorm they decorate.

Draw a model that represents the ratio of different colored streamers.
Draw a model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.

Answers

The model for representing the ratio of the number of orange and green rolls are  [tex]\dfrac{3}{2}[/tex].

A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms will be 3O=2G

What is ratio?

The ratio is defined as the representation of the one number with respect to the other number. or one number is how many times to the other number.

A model that represents the ratio of different colored streamers.

[tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex]

A model that shows the number of orange and green streamers needed to decorate 3 dorm rooms.

D=3O   and  D=2G

3O=2G

Hence the models are  [tex]\dfrac{O}{G}=\dfrac{3}{2}[/tex]  and  3O=2G.

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b) In one year, Clara and Dave borrowed books from a library in the ratio 3:7. Dave borrowed 35 books. Work out the number of books borrowed by Clara.​

Answers

3:7 =

3/7

3/7 = x/35

7x = 105

x = 15

answer : clara borrowed 15 books

I think it would be 15, because 3 doesn't go in evenly into 35. You might have the order of the ratio messed up.

Lorena paid $450 for a sneaker and there is a 9% advertised discount. What is the discount price?

Answers

Answer:

$40.50

Step-by-step explanation:

9% of 450 is 40.5

answer: $409.50

ok so, original price 450. 9% discount. discount price is the price after discount, so lets find the discount value. 9% of 450 is 40.5. now subtract that from the original price of 450. 450-40.5=409.50

205000 seconds to a year

Answers

Answer:

theres 31536000 seconds in a year

Answer:

0.0065 calendar year

Step-by-step explanation:

How many seconds makes a year?

it is 31,536,000 seconds

for an approximate result, divide the time value by 3.154⁷

therefore 205000/3.154⁷

=0.00649

=0.0065

what is the measurement of angle c

Answers

Answer: 29

Step-by-step explanation:

all triangles equal to 180

180-97-54=29

29 because u subtract the other angles from 180 and it's what is left

How many full cases and additional items are needed to fulfill the order

Answers

There are 13 full cases and 2 additional items needed to fulfill the order

How to determine the full cases and additional items?

The given parameters are:

Items ordered = 80Items per case = 6

The number of cases is:

Case = 80/6

Evaluate

Case = 13 Remainder 2

This means that:

The full case is 13 and the additional item is 2

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Evaluate the difference quotient
f(x)-f(1)/X-1, where f(x)=X +5/x+1

Answers

Answer:

C) [tex]\displaystyle\frac{-2}{(x+1)}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{f(x)-f(1)}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{1+5}{1+1}}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{6}{2}}{x-1}\\\\\frac{\frac{2(x+5)}{2(x+1)}-\frac{6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2(x+5)-6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2x+10-6x-6}{2(x+1)}}{x-1}\\\\\frac{\frac{-4x+4}{2(x+1)}}{x-1}\\\\\frac{\frac{-4(x-1)}{2(x+1)}}{x-1}\\\\\frac{-4}{2(x+1)}\\ \\\frac{-2}{(x+1)}[/tex]

8th grade distributive property equations and solutions ​

Answers

The value of x will be given as for the given expression X = -1

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

2x  +  12  =  10

2x  =  10 - 12

2x  =  -2

x    =   -1

first you distribute 2 to x and 6 which equals 2x+12=10 then you subtract 12 from 10 which equals 2x=-2 then divide -2 by 2x to see what x equals so x=-1

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The mean weight of college students is 154 lbs and the standard deviation is 3 lbs.
Assuming that the weight is normally distributed, determine the following percentages.
145 148
151
154 157 160 163
DO NOT write % in the box. It is already written outside the box for you"
The percentage of college students who weigh...
30
1)...less than 157 is
%
2) greater than 148 is
3)...between 145 and 160 is
%
%

Answers

Answer:(approx) 6.

Step-by-step explanation:Here μ=51 and σ=15

Z=

σ

X−μ

=

15

X−151

When X=120, Z=

15

120−151

=−2.067

When X=155, Z=

15

155−151

=0.2667

When X=185, Z=

15

185−151

=

15

35

=2.2667

(i) P(120<X<155)=P(−2.07<Z<0.27)

=∫

−2.067

0.2667

ϕ(z)dz=∫

0

0.2667

ϕ(z)dz+∫

0

2.0667

ϕ(z)dz

=0.4803+0.1026=0.5829.

Here N=500

∴ The number of students whose weight is between 120 and 155 pounds is

0.5872×500=291

(ii) P(X<185)=P(Z>2.27)=∫

2.2667

ϕ(z)dz

=∫

0

ϕ(z)dz−∫

0

2.2667

ϕ(z)dz=0.5−0.4881=0.0119

∴ the number of students with weight about 185 pounds.

=0.0119×500= (approx) 6.

The table below shows the distribution of votes for Student Government President elections.

1.What is the probability that a junior voted for Dao?

2.Voted for Wolber

3.Votes for Keegan and was from the sophomore class.

Answers

Answer:

1 out of 3 people vote for junior

Step-by-step explanation:

Simplify the equation √-42×√-30

Answers

Answer:

-6 [tex]\sqrt{35}[/tex]

Step-by-step explanation:

Answer:

[tex]6\sqrt{35}i[/tex]

Step-by-step explanation:

Find the area of the figure. Round to the nearest hundredth where necessary.
22 ft
30 ft

Answers


[tex]\bold{ANSWER:}[/tex]
215.20 ft^2

[tex]\bold{SOLUTION:}[/tex]

What is the answer?










.......................................................

Answers

An expression is defined as a set of numbers, variables, and mathematical operations. The expressions can be arranged as shown below.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.


According to the number of terms, the expressions can be arranged as,

x+3-y-6   ⇒ 4 terms8x+(2/3)x+6  ⇒3 terms2x+5(3x²)  ⇒ 2 terms3x⁹  ⇒ 1 ter,

Hence, the expressions can be arranged as shown above.

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If you want to make a comment that won’t be seen in r console (output) use .. what
#
print (“ “)
sum ()
rflip()

Answers

Answer: A) #

Detailed Explanation:

A ‘#’ can be used in Python to comment out a piece of code that you don’t want to run, to write down specific comments for specific blocks of code etc.

NO LINKS!! Please help me with this graph. Part 2​

Answers

Answer:

[tex]\large{\boxed{\sf y = \dfrac{2}{3} | x -6|- 7}}[/tex]

Explanation:

Absolute value of a graph formula:

y = a |x -h| + k

Identify the vertex : (h, k) = (6, -7)

Take two points: (6, -7), (9, -5)

 [tex]\sf Find \ slope \ (a) : \sf \ \dfrac{y_2 - y_1}{x_2- x_1} \ = \ \ \dfrac{-5-(-7)}{9-6} \ = \ \ \dfrac{2}{3}[/tex]

Join them to build the equation:   [tex]\bf{y = \dfrac{2}{3} |x - 6| - 7}[/tex]

Answer:

[tex]g(x)=\dfrac{2}{3}|x-6|-7[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]

-----------------------------------------------------------------------------------------

Parent function:  [tex]f(x)=|x|[/tex]

[tex]f(0)=|0|=0 \implies \textsf{The vertex of the parent function is at (0, 0)}[/tex]  

From inspection of the graph, the vertex of the transformed function is at (6, -7).  Therefore, there has been a translation of:

6 units right7 units down

[tex]\textsf{6 units right}\implies f(x-6) =|x-6|[/tex]

[tex]\textsf{and 7 units down}\implies f(x-6)-7=|x-6|-7[/tex]

From inspection of the graph, we can see that it has been stretched parallel to the y-axis:

[tex]\implies a\:f(x-6)-7=a|x-6|-7[/tex]

The line goes through point (0, -3)

Substituting this point into the above equation to find [tex]a[/tex]:

[tex]\implies a|0-6|-7=-3[/tex]

[tex]\implies 6a=4[/tex]

[tex]\implies a=\dfrac{2}{3}[/tex]

Therefore,

[tex]\implies g(x)=\dfrac{2}{3}|x-6|-7[/tex]

9 hundreds 5 ten thousands
9 ones

Answers

Answer:

50,909

Sort the digits out from greatest to least, and form a number.

The number 92,581 is represented in standard form as the sum of its place values: 90,000 + 2,000 + 500 + 80 + 1.

Standard form is a way to represent numbers using digits.

In standard form, each digit's value is determined by its position in the number.

Given 9 ten thousands + 2 thousands + 5 hundreds + 8 tens + 1 one.

9 ten thousands means we have 9 sets of ten thousands, which is 9 × 10,000 = 90,000.

2 thousands means we have 2 sets of thousands, which is 2 × 1,000 = 2,000.

5 hundreds means we have 5 sets of hundreds, which is 5 × 100 = 500.

8 tens means we have 8 sets of tens, which is 8 × 10 = 80.

1 one is the value 1.

Now, let's add up all these values:

90,000 + 2,000 + 500 + 80 + 1

= 92,581.

So, the number 92,581 is represented in standard form as the sum of its place values: 90,000 + 2,000 + 500 + 80 + 1.

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Complete question:

Write the number in standard form.

9 ten thousands +2 thousands +5 hundreds + 8 tens +1 one

Ask an expert 2+3/10X>=13/20 Solve for inequality Thanks!

Answers

Answer:

The answer is in the picture.

Step-by-step explanation:

[tex]2+\frac{3}{10x}\geq\frac{13}{20} \\\\\frac{3}{10x}\geq\frac{13}{20} -2 \\\\\frac{3}{10x}\geq\frac{13}{20} -\frac{40}{20} \\\\\frac{3}{10x}\geq-\frac{27}{20} \\\\3\geq-\frac{27}{20}*10 x \\\\3\geq-\frac{270}{20} x\\\\3\geq-\frac{27}{2} x \\\\3*-\frac{2}{27} \leq x\\\\-\frac{6}{27} \leq x\\\\-\frac{2}{9} \leq x[/tex]

Also x cannot equal to 0 if you plug in into the original equation the answer is indefinite/not solution.

4x4 y3 + v y + 7

Leading term:

Leading coefficient:

Constant term:

Answers

Answer:

Leading term: 4x⁴y³

Leading coefficient: 4

Constant term: 7

The leading term contains the highest degree and power of variable.The leading coefficient is the number written in front of the variable with the largest exponent.The constant term is the simplified number written where there are no variables.

Answer:

Leading terms : 4x⁴y³

Leading co-efficient: 4

Constant: 7

Step-by-step explanation:

Leading term: Leading term is the term that holds the highest degree of the  polynomial.

     

Leading co-efficient is the coefficient of the leading term.

Constant term is the term without any variable

Please help me with my question!​

Answers

Positive and Negative Numbers on the Number Line

When we add two negative numbers, the result will be negative.

When we add a negative and a positive number, the result can be positive, negative, or equal to zero.

Take the absolute values of both numbers (disregard their signs). If the number that was positive is greater, then the result will be positive.If the number that was negative is greater, then the result will be negative.If the two numbers are equal, then the result will be 0.

When we add two positive numbers, the result will be positive.

Solving the Questionj + k

These are both negative numbers. We know this because they are both to the left of 0. When we add two negative numbers, we will get a result that is less than 0.

Less than 0

k + n

k is a negative number while n is a positive number.

Notice that on the number line, k and n appear to be at a equal distance away from 0. This means that if we were to take their absolute values, they would be equal.

This means that adding k and n would result in an answer of 0.

Equal to 0

m + n

m is a negative number while n is a positive number.

Notice that on the number line, n appears to be further away from 0 than m is. m is very close to 0.

This means that the absolute value of n would be greater than that of m. The result would therefore be positive

Greater than 0

k + m

Both these numbers are negative. Adding them would produce a negative result.

Less than 0
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